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New Numerical Integration Formulations for Ordinary Differential Equations
Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Istanbul, Türkiye
- 1 Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Istanbul, Türkiye
Advances in Pure Mathematics·Volume 14 (2024)·Pages 650–666·Published 22 August 2024·DOI10.4236/apm.2024.148036
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Abstract
An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms satisfying different conditions are employed to generate a number of formulations. Performances of the new schemes are tested against well-known numerical integrators for selected test cases with quite satisfactory results. Convergence and stability issues of the new formulations are not addressed as the treatment of these aspects requires a separate work. The general approach introduced herein opens a wide vista for producing virtually unlimited number of formulations.
KeywordsSingle- and Multi-Step Numerical IntegrationUnconventional Base-FunctionsOrdinary Differential Equations
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